We introduce a distinctive feature of spin-polarized transport, the spin Coulomb drag: there is an intrinsic source of friction for spin currents due to the Coulomb interaction between spin ''up'' and spin ''down'' electrons. We calculate the associated ''spin trans-resistivity'' in a generalized random-phase approximation and show that, to the leading order in the interactions, it has no contribution from correlated impurity scattering. We show that, in an appropriate range of parameters, such resistivity is measurable, and we propose an experiment to measure it.Interest in spin-polarized transport has been growing dramatically in the past few years, spurred by the hope of realizing practical spin-electronic devices in a not too distant future. 1 In particular, it has been shown that spin coherence can be maintained over large distances ␦ s տ100 m and for long times T 2 ϳ10 Ϫ9 Ϫ10 Ϫ8 s both in metals 2 and in semiconductors. 3 In this paper we introduce a distinctive feature of spinpolarized transport: in a conductor, due to the Coulomb interaction, there is an intrinsic mechanism for friction between electrons of different spin, the ''spin Coulomb drag'' ͑SCD͒. For simplicity, we shall restrict our discussion to the case in which the spin state of each electron can be classified as ''up'' or ''down'' relative to the z axis. In the absence of impurities, the total momentum Pϭ ͚ i p i , where p i is the momentum of the ith electron, is a conserved quantity. On the contrary, the ''up'' and the ''down'' components of the total momentum, P ↑ ϭ ͚ i p i↑ (1ϩˆz i )/2 and P ↓ ϭ ͚ i p i↓ (1 Ϫˆz i )/2, where ˆz i is the the Pauli matrix for the z component of the ith electron's spin, are not separately conserved even in the absence of impurities: Coulomb scattering can transfer momentum between spin-up and spin-down electrons thereby effectively introducing a ''friction'' for relative motion of the two spin components. If, for example, one of the two spin components is set into motion relative to the other, it will tend to drag the latter in the same direction. Or, if a finite spin current is set up through the application of an external field, then the Coulomb interaction will tend to equalize the net momenta of the two spin components, causing the difference ͗P ↑ ͘Ϫ͗P ↓ ͘ to decay to zero when the external field is turned off.The most dramatic manifestation of the SCD is the appearance of a finite trans-resistivity defined as the ratio of the gradient of the spin-down electrochemical potential to the spin-up current density when the spin-down current is zero. This is completely analogous to the trans-resistivity measured in Coulomb drag experiments with electrons in two separate layers, 4-6 but in this case what makes the two electron populations distinguishable is not a physical separation but the different spin. In SCD, the nonconservation of the spin, caused mainly by the spin-orbit interaction, represents a ''leakage'' mechanism analogous to the interlayer tunneling in the usual Coulomb drag.First of all, let us de...